Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14555498 | C2 | semidirect |
| 2. #22577974 | C2 | semidirect |
| 3. #22577878 | C2 | semidirect |
| 4. #22577616 | C2 | semidirect |
| 5. #22577606 | C2 | semidirect |
| 6. #22577431 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577399 | C2 | semidirect |
| 14. #17984086 | C22 | semidirect |
| 15. #17984075 | C22 | semidirect |
| 23. #17984017 | C22 | semidirect |
| 24. #17984013 | C22 | semidirect |
| 25. #17984012 | C22 | semidirect |
| 26. #17984009 | C22 | semidirect |
| 116. C137 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555498 | 2 |
| #22577974 | 2 |
| #22577878 | 2 |
| #22577616 | 2 |
| #22577606 | 2 |
| #22577431 | 2 |
| #22577413 | 2 |
| #22577399 | 2 |
| C2×AGL(1,ℤ/8)×C137 | 2 |
| #3042 | 137 |